Hello! I've seen a few other questions pertaining to this dilemma but I have not found any accurate answers or ways to solve this problem (probably because I was not smart and did not bother to research possible side effects when I tried this).
So on my 3ds I have a standard 4 GB SD card w/ my all my data on it. When Pokemon Alpha Sapphire came out I did not have enough data to download it without deleting another game (and being very short-sighted I did not think to delete something and create back-up data and re-installing when I was able to upgrade) and downloaded it instead to a separate 2 GB SD card spare.
I understand now that I cannot simply transfer the data over to a new separate 32 GB SD card because for some reason my downloaded games from my 4 GB SD card do not transfer over. However I noticed that in the combined 32 GB SD card some of the data did happen to transfer over when I checked Data Management in the System Settings and clicked Extra Data Management in the Nintendo 3DS category. I thought that I would be able to create Save-Data Backups for the games I wanted to transfer over and re-install them on the 32 GB SD card but they still did not end up transferring.
I have seen posts claiming that it is possible to transfer the data, but it is tedious and difficult to determine which files hold which games however I have never found a post or video showing or explaining how to do this in detail. If anyone has any idea how to solve this please let me know!
(Sorry for the long explanation and feel free to pm for more clarification if needed).